Many people have given great amounts of thought about how to heat their home in a PAW. Just doing a little out of the box thinking lead me to an idea for cooling your residence in a fairly good fashion.
Of course, this will depend greatly on whether you have some power supply, battery bank or generator, and the requisite materials to make this thing work and it is dependent on where you reside.
What I'm thinking about is known as a "swamp cooler". A simple cooling device used extensively in the southwestern US and other areas of high heat and moderate to low humidity levels.
The device I'm considering would be a frame with a blower of some sort that works with your power supply, a reasonable thickness cloth for air to pass through and water to pass over, a means of running water over the cloth and a catch device at the bottom so that the water is not wasted.
The cloth is attached at the top of the frame with a tube manifold running across the top so that the water can be directed to drip down and into the cloth and has a valve to regulate the flow. The cloth is secured so that it does not get drawn into the blower but is not terribly tight, just enough to hold its position.
The water would flow by gravity by being poured into a reservoir above the cloth and the valve adjusted for a working flow. The blower would just move the air through the watered cloth and would provide some cooling to the space by evaporation.
I don't have any diagrams or pictures but, I may make a drawing just to show it off.
With a 12v blower out of a vehicle there ought to be plenty of air to provide some cooling.